There is no garrison prerequisite. There was a logic error with the Challenge mode quests that could cause the daily randomizer to select an invalid value (and thus leave no quest available for the day), and we have a hotfix in flight to address that issue.

Also, since I've seen this come up a few times, the currency turn-in quests for the Tempered Seals of Fate that are used for Draenor bonus rolls are not available until the first raid zone, Highmaul, unlocks during the week of December 2. Take your time and enjoy Draenor; no need to worry about having to stockpile bonus rolls ahead of time.